/*
Given an array of non-negative integers and a value sum,
determine the total number of the subset with sum
equal to the given sum.
*/
/*
 Given solution is O(n*sum) Time complexity and O(sum) Space complexity
*/
function NumberOfSubsetSum( array, sum ) {
  const dp = [] // create an dp array where dp[i] denote number of subset with sum equal to i
  for ( let i = 1; i <= sum; i++ ) {
    dp[ i ] = 0
  }
  dp[ 0 ] = 1 // since sum equal to 0 is always possible with no element in subset

  for ( let i = 0; i < array.length; i++ ) {
    for ( let j = sum; j >= array[ i ]; j-- ) {
      if ( j - array[ i ] >= 0 ) {
        dp[ j ] += dp[ j - array[ i ] ]
      }
    }
  }
  return dp[ sum ]
}

function main() {
  const array = [ 1, 1, 2, 2, 3, 1, 1 ]
  const sum = 4
  const result = NumberOfSubsetSum( array, sum )
  console.log( result )
}
main()
